Durbin spoke Monday at an event sponsored by the Chicago Council on Global Affairs.
The Democrat asked Boehner and other House Republicans not to kill the immigration bill that the Senate passed last month.
"We had a strong bipartisan bill in the Senate. The only way this can pass the House of Representatives is bipartisan support. I hope the speaker will reach out and ask both parties to come together as we did in the Senate and come up with a good approach. Then we can sit down and work out our differences," said Sen. Durbin.
The bill would provide millions of illegal immigrants with a path to citizenship.
House Republicans meet Wednesday to decide their next step.